Not applicable.
This invention relates generally to electrical circuits and more particularly to circuits that model the behavior of biological neurons.
As is known in the art, there exists a class of networks referred to as neural networks which model the behavior of certain human functions. Electronic neural networks have been used to implement mathematical or engineering abstractions of biological neurons. Circuits emulating biological neurons are typically implemented using digital circuits that operate up to a million times faster than actual neurons or with software which simulates the behavior of a biological neuron. One problem with the digital circuit approach, however is that it does not utilize life-like principles of neural computation. Furthermore, a biological nervous system contains thousands or millions of interconnected neurons and thus the complexity of a biological nervous system results in a complex digital circuit.
Similarly, given the complexity of the biological systems, software simulations can take many hours or days even using presently available state-of the-art processing systems. Thus software systems are not appropriate for use in applications which require real time or close to real time performance from such systems.
An electronic circuit that emulates the analog behavior of actual biological neurons, on the other hand, can perform simulations in real time. Thus, to overcome the above limitations with systems implemented using digital circuits or software, electronic circuit neural networks which use principles of neural computation which are more life-like than the digital circuit or software approaches have been developed.
This type of neural network interacts with real-world events in a manner which is the same as or similar to biological nervous systems and can be utilized in a variety of systems including but not limited to electronic and electromechanical systems, such as artificial vision devices and robotic arms. Such neural networks can also be used as research tools to better understand how biological neural networks communicate and learn.
Much of the effort directed toward producing electronic implementations of biological neurons have focused on emulating the input-output functional characteristics of the neuron, essentially treating the neuron as an abstracted black box. These implementations focus on circuits and techniques for generating an action potential in an attempt to simulate the actions neurons take to communicate with one another. One problem with past approaches, however, is that such approaches fail to properly take into account or model the means which actually produces the action potential in a biological neuron.
Some prior art techniques have produced analog integrated circuits that mimic the functional characteristics of real neuron cells, by isomorphically emulating the membrane conductances within an actual neuron cell body. Thus, one problem with prior art approaches is that they fail to include circuitry for the synapse through which neurons communicate and/or the prior art approaches fail to include circuitry for the dendrite which is the connection between the synapse and neuron cell body. Prior art systems also fail to include effective circuitry to implement the adaptation or learning functions of real neurons.
As known to one of ordinary skill in the art, a neuromorphic system emulates the functionality and organization of a biological nervous system on an integrated circuit. Neuromorphic systems typically include analog electronic circuits with digital circuitry to enhance and support their function. Fabrication of these neuromorphic circuits is most often done in a complementary-metal-oxide-semiconductor (CMOS) process using very large-scale integration (VLSI) technology.
Neuromorphic systems directly embody in the physics of their analog CMOS circuit building blocks so-called isomorphisms of the biophysical processes. Neural computational primitives like amplifying, exponentiating, thresholding, integrating, taking the sigmoidal function of, and storing charge, can thus be efficiently performed in a real-time analog fashion using compact low-power CMOS circuits designed specifically for these purposes.
Digital computing paradigms in other fields of science and engineering has led to their use in simulating nervous systems. Digital simulations by themselves, however, require huge and complex Boolean logic functions encode fundamentally analog neural computational primitives, such as those mentioned above. Thus, the modeled system must be translated into an explicitly mathematical form. This is grossly inefficient in terms of time and number of transistors required to execute a neural computation. Significantly, the natural temporal relationship between neuronal processes is not preserved in a digital simulation on a computer thereby preventing real time interaction with the real world in a manner analogous to that of biological nervous system.
Animal nervous system are capable of learning and remembering. One simple type of learning involves the interaction of two neurons, as shown in FIG. 1. Learning occurs when there is an alteration of the synaptic transmission strength from the presynaptic neuron""s axon terminal to the postsynaptic neuron""s synapse head. A synapse whose strength can be modified by neuronal activity is said to be plastic, and the general phenomenon is known as synaptic plasticity. When neuronal activity leads to an increase in synaptic transmission strength, the synapsc is said to have become potentiated. And when this stimulation leads to a decrease in strength, the synapse is said to have become depressed. If these changes are subsequently retained, the xe2x80x9clearnedxe2x80x9d information is xe2x80x9crememberedxe2x80x9d by the synapse. Potentiation that is retained for a long period of time after neuronal activity has ceased is known as long-term potentiation (LTP). Likewise, depression that is retained for a long period of time after neuronal activity has ceased is known as long term depression (LTD). Both of these phenomena have been shown to occur in the various regions of the brain.
One known electrical model that attempts to explain the biophysical behavior of a Hebbian synapse is shown in FIG. 2. Examining the simple two-neuron system of FIG. 1, when the presynaptic neuron fires an action potential, its axon terminal release neurotransmitters. These neurotransmitters pass through the synaptic cleft and bind to receptors on the synapse head. This causes NMDA and non-NMDA ion channels to open up. The NMDA ion channel passes an electric current, which consists primarily of Ca2+ ions. This postsynaptic influx of Ca2+ ions plays a pivotal role in the expression of synaptic plasticity. Upon entering the synapse head, Ca2+ ions set in motion a series of events that ultimately leads to the induction and maintenance of LTP and/or LTD.
FIG. 3 shows how the level of calcium concentration that has accumulated inside of a synapse operates to change the long-term plasticity. The non-NMDA ion channels pass a current which, in contrast to the NMDA channels, consists mainly of Na+ ions (with a negligible Ca2+ component). The total synaptic current that flows through the membrane thus consists of the sum of (1) the NMDA current, and (2) the non-NMDA current; plus (3) a small leakage current, and (4) a capacitive current that flows when the head membrane voltage is changing.
The leakage conductance ghead is constant while the non-NMDA conductance gnon-NMDA is dependent on the time that elapses after an action potential excites the synapse. It is given by the following alpha-function             g              non        -        NMDA              ⁡          (      t      )        =      κ    ⁢          xe2x80x83        ⁢          g      p        ⁢    t    ⁢          xe2x80x83        ⁢          exp      ⁡              (                              -            t                                t            p                          )            
where xcexa=e/tp, e is the base of the natural logarithm, tp=1.5 ms, and the peak conductance gp=0.5 nS. The concentration of calcium within the synapse also modulates this conductance, and that this is the biophysical mechanism by which LTP and LTD are expressed
Like the non-NMDA conductance gnon-NMDA, the NMDA conductance gNMDA also depends on the time that elapses after an action potential excites the synapse. However, there is an additional dependence on the synapse head membrane voltage Vhead, and there is no dependence on calcium concentration. In this case, the conductance is a sigmoidal function             g      NMDA        ⁡          (      t      )        =                    exp        ⁡                  (                                    -              t                                      τ              1                                )                    -              exp        ⁡                  (                                    -              t                                      τ              2                                )                            1      +                        η          ⁡                      [                          Mg                              2                +                                      ]                          ⁢                  exp          ⁡                      (                                          -                γ                            ⁢                              xe2x80x83                            ⁢                              V                head                                      )                              
where xcfx841=80 msec, xcfx842=0.67 msec, xcex7=0.33/mM, xcex3=0.06 mV, and gxcex7=0.2 nS. When Vhead is near its resting potential, the NMDA ion channel conductance is close to zero and little Ca2+ enters the cell. Excitation by action potentials from the presynaptic neuron, however, causes the conductance of the non-NMDA ion channels to increase. This allows an influx of Na+ ions into the synapse head which charges up the membrane capacitance Ch and increases the membrane voltage Vhead. The increase in Vhead in turn causes the conductance of the NMDA channels to rise from zero, allowing an influx of calcium ions that induces LTP and/or LTD or neither, as shown in FIG. 3.
Three broad types of LTP and LTD may be distinguished: hemosynaptic, associative, and heterosynaptic. Homosynaptic LTP and homosynaptic LTD occur in isolated synapses, such as the 2-neuron system of FIG. 1. Homosynaptic LTP is induced when a single synapse is subjected to a burst of high frequency action-potential stimulation from a presynaptic neuron. This type of LTP can be thought of as a sort of microscopic xe2x80x9cpractice makes perfect.xe2x80x9d That is, memory is reinforced through repeated use of the synapse.
Homosynaptic LTD, on the other hand, occurs when the synapse is subjected to a long period of sustained low frequency stimulation. While it may not be intuitive that repeated use of a synapse even at low frequencies result in a synaptic depression, the biological significance makes sense if one considers this sort of LTD to be a microscopic xe2x80x9cgetting so use to something you forget about itxe2x80x9d. As an example, consider the buzzing of fluorescent lights. To someone not used to working in a room with them, they can be quite distracting. But after awhile, this sensitivity disappears.
FIG. 4 summarizes the experimentally determined long-term plasticity behavior of a synapse, e.g. the simple two neuron system of FIG. 1, when it is subjected to a range of presynaptic action potential frequencies. The synaptic strength is a result of the operation of Ca2+ within the synapse, as described above.
It would, therefore, be desirable to provide a neuromorphic circuit that emulates homosynaptic long term potentiation and long term depression.
In accordance with the present invention, a circuit which implements functions of a biological nervous system includes a plurality of neuron circuits and a plurality of synapse circuits. The synapse circuits are coupled to provide a path through which the plurality of neuron circuits communicate. Each of the plurality of neuron circuits include (1) a neuron cell membrane circuit, (2) a learning circuit coupled to said neuron cell membrane circuit; and (3) a dendrite circuit coupled to the neuron cell membrane circuit. Each of the synapse circuits include means for modifying the synaptic conductance With this particular arrangement, a neuron circuit which models a biological neuron circuit and in particular which emulates the neuron synapse is provided. By providing the neuron circuit with circuitry which allows adaptation or learning function to be performed, the neuron circuit of the present invention more closely models a biological neuron than prior art systems. The synapse circuit includes an NMDA channel circuit which is coupled in parallel with a non-NMDA channel circuit between first and second terminals of the synapse circuit. Also coupled in parallel between the first and second terminals of the synapse circuit in parallel with the NMDA and non-NMDA channel circuits is a storage element. The non-NMDA channel circuit controls the induction of LTP and LTD in the neuron circuit thereby emulating the response to a neurotransmitter in a biological neuron. In particular, the induction of LTP is characterized by a prolonged increase in the conductance of the non-NMDA receptor channel, while the induction of LTD is characterized by the decrease in conductance of the non-NMDA receptor channel. The NMDA channel circuit provides a current which is approximately proportional to the flow of magnesium ions (Ca2+) into the spine head. The NMDA circuit emulates the response to the neurotransmitter. This controls long term memory effects in biological systems. The response to the post-synaptic neuron gives a pairing effect meaning that an NMDA receptor receives signals from both pre- and post-synaptic neurons and provides a response thereto. In a biological neuron, non-NMDA xe2x80x9cchannelsxe2x80x9d carry sodium ions (Na+) which are abundant while NMDA xe2x80x9cchannelsxe2x80x9d regulate the flow of calcium ions (Ca2+)to the neuron. The calcium is the internal messenger. Once the calcium travels into the cell body, it triggers chemical reactions (referred to as xe2x80x9csecondary messengersxe2x80x9d) in the post-synaptic cell. These secondary messengers affect the non-NMDA channels by increasing or decreasing the transmission in the channel. The neuron circuit of the present invention emulates the calcium influx via the NMDA channels and generates a signal which controls the response of the non-NMDA circuits by controlling the number of channels in those circuits which are open or closed.
In accordance with a further aspect of the present invention, an integrated circuit which implements functions of a biological nervous system includes circuits designed to emulate the electrical characteristics of actual neurons. In particular, the circuits emulate the neuron cell membrane, the dendritic structure, and a synapse. In one embodiment, one particular type of synapse referred to as a Hebbian synapse is modeled. These circuits are more neuromorphic compared to most analog neural networks. The neuron cell membrane circuits include circuitry to represent the sodium and potassium ion channels in the membrane. The synapse circuits include circuit portions which correspond to different types of synaptic current channels. Moreover the neuron circuit design of the present invention includes circuits which modify the synaptic conductance, or strength of the neuron through a feedback mechanism. With this particular technique, an analog CMOS circuit implementation of an electrical model of a biological synapse is provided. In particular, the circuits emulate the synaptic modification, the learning mechanism, exhibited in certain types of neurons. This can be used in an artificial neural network that emulates neural computation in a manner which is more realistic than conventional electronic artificial neural networks. In one embodiment, the integrated circuit of the present invention is implemented using CMOS circuits.
In accordance with another aspect of the invention, an LTP/LTD controller circuit includes a circuit for controlling the conductance level of the synapse circuit. The conductance level corresponds to the number of conductive pathways associated with a non-NMDA ion channel circuit. Each of the conductive pathways includes a switching element that has a conduction state determined by a respective control signal. In one embodiment, the controller circuit includes a counter that loads the conductance value of a synapse, i.e., the number of conductive pathways, which is determined by the switching element control signals. The counter increments, decrements, or does not change, the synapse conductance value based upon the state of a plurality of counter control signals that correspond to the synapse calcium concentration level.